Applications of polynomial systems
- Responsibility
- David A. Cox ; with contributions by Carlos D'Andrea, Alicia Dickenstein, Jonathan Hauenstein, Hal Schenck, Jessica Sidman
- Publication
- Providence, Rhode Island : Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, [2020]
- Physical description
- ix, 250 pages : illustrations (some color) ; 26 cm
- Series
- Regional conference series in mathematics ; no. 134.
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| Call number | Status |
|---|---|
| QA1 .R33 NO.134 |
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Description
Creators/Contributors
- Author/Creator
- Cox, David A., author.
- Contributor
- D'Andrea, Carlos (Carlos Antonio), 1973- author.
- Dickenstein, Alicia, author.
- Hauenstein, Jonathan D., author.
- Schenck, Henry K., 1963- author.
- Sidman, Jessica, author.
- Conference Board of the Mathematical Sciences, issuing body.
- National Science Foundation (U.S.), sponsoring body.
- NSF-CBMS Regional Conference in the Mathematical Sciences (2018 : Fort Worth, Tex.)
Contents/Summary
- Bibliography
- Includes bibliographical references (pages 225-241) and index
- Contents
-
- Elimination theory Numerical algebraic geometry Geometric modeling Rigidity theory Chemical reaction networks Illustration credits Bibliography Index.
- (source: Nielsen Book Data)
- Summary
-
Systems of polynomial equations can be used to model an astonishing variety of phenomena. This book explores the geometry and algebra of such systems and includes numerous applications. The book begins with elimination theory from Newton to the twenty-first century and then discusses the interaction between algebraic geometry and numerical computations, a subject now called numerical algebraic geometry. The final three chapters discuss applications to geometric modeling, rigidity theory, and chemical reaction networks in detail. Each chapter ends with a section written by a leading expert. Examples in the book include oil wells, HIV infection, phylogenetic models, four-bar mechanisms, border rank, font design, Stewart-Gough platforms, rigidity of edge graphs, Gaussian graphical models, geometric constraint systems, and enzymatic cascades. The reader will encounter geometric objects such as Bezier patches, Cayley-Menger varieties, and toric varieties; and algebraic objects such as resultants, Rees algebras, approximation complexes, matroids, and toric ideals. Two important subthemes that appear in multiple chapters are toric varieties and algebraic statistics. The book also discusses the history of elimination theory, including its near elimination in the middle of the twentieth century. The main goal is to inspire the reader to learn about the topics covered in the book. With this in mind, the book has an extensive bibliography containing over 350 books and papers.
(source: Nielsen Book Data)
Subjects
- Subject
- Polynomials > Congresses.
- Commutative algebra > Congresses.
- Geometry, Algebraic > Congresses.
- Commutative algebra.
- Geometry, Algebraic.
- Polynomials.
- Commutative algebra -- Computational aspects and applications [See also 14Qxx, 68W30] -- Solving polynomial systems; resultants.
- Algebraic geometry -- Computational aspects in algebraic geometry [See also 12Y05, 13Pxx, 68W30] -- None of the above, but in this section.
- Commutative algebra -- Computational aspects and applications [See also 14Qxx, 68W30] -- Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)
- Algebraic geometry -- Special varieties -- Toric varieties, Newton polyhedra [See also 52B20].
- Convex and discrete geometry -- Discrete geometry -- Rigidity and flexibility of structures [See also 70B15].
- Statistics -- Multivariate analysis [See also 60Exx] -- None of the above, but in this section.
- Numerical analysis -- Nonlinear algebraic or transcendental equations -- Global methods, including homotopy approaches [See also 58C30, 90C30].
- Computer science {For papers involving machine computations and programs in a specific mathematical area, see Section--04 in that area} -- Computing methodologies and applications -- Computer-aided de.
- Biology and other natural sciences -- Physiological, cellular and medical topics -- Systems biology, networks.
Bibliographic information
- Publication date
- 2020
- Series
- Conference Board of the Mathematical Sciences CBMS regional conference series in mathematics, 0160-7642 ; number 134
- Note
- "With support from the National Science Foundation."
- "The five chapters are based on the NSF-CBMS Regional Research Conference Applications of Polynomial Systems held at Texas Christian University June 4-8, 2018."
- ISBN
- 9781470451370 paperback
- 1470451379 paperback
- 9781470455897 electronic book
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